"given a function defined by" is irrelevant. At t=3 (t-3)/(t-3) is undefined.

> I've already shown that a modified version of that> proposition does make sense.

No you haven't.

> Given a function f(t) continuous for all real numbers t and defined by> (t^2-9)/(t-3) everywhere the expression is meaningful, that function is> identical to g(t) = (t+3). My original mistake was to assume continuity> after using (t^2-9)/(t-3) to define the entire function.

What you wish to say is that the function g:R->R defined by

g(t) = f(t) if t=/=3 = 6 otherwise

has these properties:i) g = f where f is defined,ii) g is defined on the whole of R,iii) g is continuous.

-- The world will little note, nor long remember what we say hereLincoln at Gettysburg